The fossil record clearly shows the evolutionary progression from early aquatic vertebrates to mammals. The earliest known fossil vertebrates were heavily armored fish discovered in rocks from the Ordovician Period about 500 to 430 million years ago. (The phrase 'million years ago' is shortened to 'mya' in most paleontological references). The Devonian Period (395 to 345 mya) brought in the changes that allowed primitive lungfish to remain on land as long as they wished, thus becomng the first terrestrial vertebrates, the amphibians.
Amphibians developed forms of reproduction and locomotion and a metabolism better suited for life exclusively on land, becoming more reptilian. Full fledged reptiles appeared in the Carboniferous Period (345 to 280 mya).
The reptilian changes and adaptations to diet and geography are chronicled in the fossil record of the varying forms of therapsids. True mammals showed up in the Triassic Period (225 to 190 mya) around the same time as the dinosaurs, which also sprouted from the reptilian line.
One of the people who helped figure out this progression was French zoologist Baron Georges Cuvier (1769-1832) who realized that fossils found in older rock stratas differed greatly from more recent fossils or modern animals. He published his findings in 1812 and although he steadfastly refuted evolution, his work proved the (at the time) heretical theory of extinction of species.
Paleontology really got started though, with the publication of Recherches sur les poissons fossils (1833-1843) by Swiss naturalist Louis Agassiz (1807-1873). He studied, described and listed hundreds of species of fossil fish, beginning the serious study into the lives of extinct animals.
In modern times, some have said that Alfred Romer (1894-1973) wrote the definative textbook on the subject, called Vertebrate Paleontology, which shows the progression of evolution in fossil fish, and amphibians and reptiles through comparative anatomy. Romer became the first president of the Society of Vertebrate Paleontology in 1940. Others would claim that the current definative book on the subject was written by Robert L Carroll of McGill University in his 1988 text Vertebrate Paleontology and Evolution. Carroll was president of the Society of Vertebrate Paleontology in 1983. The Society keeps its members informed on the latest discoveries through newsletters and the Journal of Vertebrate Paleontology.
Even though some of the most brilliant, creative people who have ever lived have spent their careers advancing the field of vertebrate paleontology, the fact remains that new and previously unknown species are found every week. It becomes increasingly clear that we haven't even scratched the surface of all that we could know about the animals that lived on Earth before us.